Year: 2009
Type: preprint
Abstract: Motivated by investigations of the tridiagonal pairs of linear transformations, we introduce the augmented tridiagonal algebra ${\mathcal T}_q$. This is an infinite-dimensional associative ${\mathbb C}$-algebra with 1. We classify the finite-dimensional irreducible representations of ${\mathcal T}_q$. All such representations are explicitly constructed via embeddings of ${\mathcal T}_q$ into the $U_q(sl_2)$-loop algebra. As an application, tridiagonal pairs over ${\mathbb C}$ are classified in the case where $q$ is not a root of unity.
Source: arXiv (Cornell University)
Authors: Ito, Tatsuro, Terwilliger, Paul
Institutions: Kanazawa University, University of Wisconsin–Madison
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2018855503